A Bayesian approach to the design and analysis of fractionated experiments

Technometrics

Volumn 48, Issue 2, 2006, Pages 219-229

  Joseph, V Roshan ^a  

^a Georgia Institute of Technology   (United States)

Author keywords

Gaussian process; Minimum aberration criterion; Optimal design; Prior information; Quality engineering

Indexed keywords

GAUSSIAN PROCESS; MINIMUM ABERRATION CRITERION; OPTIMAL DESIGN; PRIOR INFORMATION; QUALITY ENGINEERING;

ABERRATIONS; INFORMATION ANALYSIS; LOGIC DESIGN; NUMERICAL ANALYSIS; OPTIMAL SYSTEMS; PARAMETER ESTIMATION;

MATHEMATICAL MODELS;

EID: 33744504939     PISSN: 00401706     EISSN: None     Source Type: Trade Journal    
DOI: 10.1198/004017005000000652     Document Type: Review

References (32)

1. Box, G. E. P., and Hunter, J. S. (1961), "The Fractional Factorial Designs," Technometrics, 3, 311-351, 449-458.
2. Box, G. E. P., and Meyer, R. D. (1993), "Finding the Active Factors in Fractionated Screening Experiments," Journal of Quality Technology, 25, 94-105.
3. Chaloner, K., and Verdinelli, I. (1995), "Bayesian Experimental Design: A Review," Statistical Science, 10, 273-304.
4. Chipman, H. (1996), "Bayesian Variable Selection With Related Predictors," Canadian Journal of Statistics, 24, 17-36.
5. _ (1998), "Fast Model Search for Designed Experiments With Complex Aliasing," in Quality Improvement Through Statistical Methods, ed. B. Abraham, Boston: Birkhäuser, pp. 207-220.
6. Chipman, H., George, E. I., and McCulloch, R. E. (2001), "The Practical Implementation of Bayesian Model Selection" (with discussion), in Model Selection, ed. P. Lahiri, IMS Lecture Notes - Monograph Series, Vol. 38, Beachwood, OH: Institute of Mathematical Statistics, pp. 65-134.
7. Chipman, H., Hamada, M., and Wu, C. F. J. (1997), "A Bayesian Variable-Selection Approach for Analyzing Designed Experiments With Complex Aliasing," Technometrics, 39, 372-381.
8. n-k Fractional Factorial Designs and Search for Minimum Aberration Designs," The Annals of Statistics, 20, 2124-2141.
9. Cheng, C. S., and Mukerjee, R. (1998), "Regular Fractional Factorial Designs With Minimum Aberration and Maximum Estimation Capacity," The Annals of Statistics, 26, 2289-2300.
10. Cheng, C. S., Steinberg, D. M., and Sun, D. X. (1999), "Minimum Aberration and Model Robustness for Two-Level Fractional Factorial Designs," Journal of the Royal Statistical Society, Ser. B, 61, 85-93.
11. Cheng, S. W., and Ye, K. Q. (2004), "Geometric Isomorphism and Minimum Aberration for Factorial Designs With Quantitative Factors," The Annals of Statistics, 32, 2168-2185.
12. Currin, C., Mitchell, T. J., Morris, M. D., and Ylvisaker, D. (1991), "Bayesian Prediction of Deterministic Functions, With Applications to the Design and Analysis of Computer Experiments," Journal of American Statistical Association, 86, 953-963.
13. Daniel, C. (1959), "Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments," Technometrics, 1, 311-341.
14. Fries, A., and Hunter, W. G. (1980), "Minimum Aberration Designs," Technometrics, 22, 601-608.
15. George, E. I., and McCulloch, R. E. (1993), "Variable Selection via Gibbs Sampling," Journal of the American Statistical Association, 88, 881-889.
16. Harville, D. A. (1997), Matrix Algebra From a Statistician's Perspective, New York: Springer-Verlag.
17. Hamada, M., Martz, H. F., Reese, C. S., and Wilson, A. G. (2001), "Finding Near Optimal Bayesian Experimental Designs via Genetic Algorithms," The American Statistician, 55, 175-181.
18. Hamada, M., and Wu, C. F. J. (1992), "Analysis of Designed Experiments With Complex Aliasing," Journal of Quality Technology, 24, 130-137.
19. Hunter, G. B., Hodi, F. S., and Eager, T. W (1982), "High Cycle Fatigue of Weld-Repaired Cast Ti-6Al-4V," Metallurgical Transactions, 13A, 1589-1594.
20. k for Bayesian Experimental Design," unpublished doctoral thesis, University of California, Los Angeles.
21. _ (2001), "Bayesian-Optimal Fractional Factorials," Statistica Sinica, 11, 605-630.
22. Li, R., and Sudjianto, A. (2005), "Analysis of Computer Experiments Using Penalized Likelihood in Gaussian Kriging Models," Technometrics, 47, 111-120.
23. Meyer, R. D., Steinberg, D. M., and Box, G. (1996), "Follow-up Designs to Resolve Confounding in Multifactor Experiments" (with discussion), Technometrics, 38, 303-332.
24. Mitchell, T. J., Morris, M. D., and Ylvisaker, D. (1995), "Two-Level Fractional Factorials and Bayesian Prediction," Statistica Sinica, 5, 559-573.
25. Montgomery, D. C. (2004), Design and Analysis of Experiments (6th ed.), New York: Wiley.
26. Neter, J., Kutner, M. H., Nachtsheim, C. J., and Wasserman, W. (1996), Applied Linear Statistical Models, Boston: McGraw-Hill.
27. Santner, T. J., Williams, B. J., and Notz, W. I. (2003), The Design and Analysis of Computer Experiments, New York; Springer-Verlag.
28. Taguchi, G. (1987), System of Experimental Design, Vols. 1 and 2, White Plains, NY: Unipub/Kraus International.
29. Tang, B., and Deng, L. Y. (1999), "Minimum G2-Aberration for Nonregular Fractional Factorial Designs," The Annals of Statistics, 27, 1914-1926.
30. Toman, B. (1994), "Bayes-Optimal Designs for Two- and Three-Level Factorial Experiment," Journal of the American Statistical Association, 89, 937-946.
31. Wu, C. F. J., and Hamada, M. (2000), Experiments: Planning, Analysis, and Parameter Design Optimization, New York: Wiley.
32. Wu, H., and Wu, C. F. J. (2002), "Clear Two-Factor Interactions and Minimum Aberration," The Annals of Statistics, 30, 1496-1511.